206 Lord Rayleigh. On the Bridge Method in its [Feb. 19, 





(1), 



the coefficient of fa in the first equation being identical with that 

 of fa in the second by the reciprocal property. The three constants 

 A, B, C are in general complex quantities, functions of j>. 



In the application that wo have to make of these equations, fa, fa, 

 *i, i'a will represent respectively currents and electromotive forces in 

 the battery and telephone branches of the combination. The re- 

 ciprocal property may then be interpreted as follows : If * = 0, 



and 



fa = 



n* 



(2). 



B 3 -AC 



In like manner, if we had supposed *i = 0, we should have found 



B 



fa = 



B 2 -AC 



(3), 



showing that the ratio of the current in one branch to an electro- 

 motive force operative in the other is independent of the way in 

 which the parts are assigned to the two branches. 



We have now to determine the constants A B, C in terms of the 

 electrical properties of the system. If fa be maintained zero by a 

 suitable force * 2 , the relation between ^i and *i is *i = -Afa. In 

 our application, A therefore denotes the (generalised) resistance to 

 an electromotive force in the battery branch, when the telephone branch 

 is open. This resistance is made up of /, the resistance in the battery 

 branch, and of that of the conductors a+c, b + d combined in 



parallel. Thus, 



(~ i_-\ fiA_j\ 



(4). 



Inlikemanner, 



C = 



a+o+c 



(4'). 



To determine B let us consider the force ^j which must act in e in 

 order that the current through it (fa) may be zero, in spite of the 

 operation of iv We have 1r t = Ufa. The total current fa flows 

 partly along the branch a+c, and partly along 6 + d. The current 

 through a + c is 



1 

 a + c 









a+c 



a+6+c+a 



b + d 





